# Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not

arXiv: https://arxiv.org/abs/2607.21645 · HTML: https://mlsanity.com/paper/2607.21645/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 12 of 12)

- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [Training Transformers with Enforced Lipschitz Constants](https://mlsanity.com/paper/2507.13338/) (2025)
- [Is the Future Compatible? Diagnosing Dynamic Consistency in World Action Models](https://mlsanity.com/paper/2605.07514/) (2026)
- [Benchmarking World-Model Learning with Environment-Level Queries](https://mlsanity.com/paper/2510.19788/) (2025)
- [Kairos: A Regret-Aware Native World-Action Model Stack for Physical AI](https://mlsanity.com/paper/2606.16533/) (2026)
- [Beyond the Next Step: Variable-Length Latent World Models for Long-Horizon Planning](https://mlsanity.com/paper/2606.21775/) (2026)
- [Toward Consistent World Models with Multi-Token Prediction and Latent Semantic Enhancement](https://mlsanity.com/paper/2604.06155/) (2026)
- [ATM: Action-Consistency Transfer Matrix for Diagnosing and Improving Latent World Models](https://mlsanity.com/paper/2606.09028/) (2026)
- [Predictive Objectives Discard Exogenous Control-Relevant Features: A Controlled Mechanistic Study](https://mlsanity.com/paper/2606.30068/) (2026)

## Abstract (arXiv)

Multi-horizon latent consistency is a common training knob in video predictors and world models, but practitioners rarely know what it does to transition geometry. We treat lambda, the weight on multi-step latent agreement, as a diagnostic control and measure an empirical expansion proxy L20,q95 together with horizon-20 prediction error E20. On Moving-MNIST (n=6 seeds at the critical pair), raising lambda from 0 to 0.8 cuts L20 from 4.96 +/- 2.01 to 1.01 +/- 0.06 (paired t p=0.005, Wilcoxon p=0.031) and halves E20 (0.365 to 0.177, paired t p=1.1e-13). Four of six seeds cross L<1 at lambda=0.8. The same loss does not produce population L<1 on action-conditioned Pendulum-v1 or CartPole-v1, nor on KTH Actions video, even when E20 improves. An associational mediation analysis on MMNIST gives r-hat=0.94 (95% CI [0.88, 1.00], n=27, B=2000); lambda was not randomized. Defensive checks (architectural baselines, exogenous stress, WorldTest, MPC, scaling) mostly support a narrow claim: soft consistency can push passive video toward a near-contractive band, and that band is domain-limited. A stochastic-forcing law L20 ~ 1.23 + 1.82 eta at lambda=0.8 (bootstrap slope CI [1.73, 1.92], R^2=0.96) unifies control domains on the same curve via calibrated eta_eff. Complete joint slices at lambda in {0.4, 1.2} (30/30 cells, 5 eta x 3 seeds) show comparable linear L20(eta) slopes (~1.69 and ~2.00); we do not fit a continuous (lambda, eta) surface. We do not report DreamerV3 or TD-MPC2 returns.